Multiplicative Binomial        package:rmutil        R Documentation

_T_h_e _M_u_l_t_i_p_l_i_c_a_t_i_v_e _B_i_n_o_m_i_a_l _D_i_s_t_r_i_b_u_t_i_o_n

_U_s_a_g_e:

     dmultbinom(y, n, m, s)
     pmultbinom(q, n, m, s)

_A_r_g_u_m_e_n_t_s:

       y: vector of frequencies

       q: vector of quantiles

       n: vector of totals

       m: vector of probabilities

       s: vector of overdispersion parameters

_V_a_l_u_e:

     These functions provide information about the multiplicative
     binomial distribution with parameters `m' and `s'. `dmultbinom'
     gives the density and `pmultbinom' gives the distribution
     function.

     The multiplicative binomial distribution with total = n and `prob'
     = m has density

        p(y) = c(n,m,s) Choose(n,y) m^y (1-m)^(n-y) s^(y(n-y))

     for y = 0, ..., n, where c(.) is a normalizing constant.

_A_u_t_h_o_r(_s):

     J.K. Lindsey

_S_e_e _A_l_s_o:

     `dbinom' for the binomial, `ddoublebinom' for the double binomial,
     and `dbetabinom' for the beta binomial distribution.

_E_x_a_m_p_l_e_s:

     # Compute P(45 < y < 55) for y multiplicative binomial(100,0.5,1.1)
     sum(dmultbinom(46:54, 100, 0.5, 1.1))
     pmultbinom(54, 100, 0.5, 1.1)-pmultbinom(45, 100, 0.5, 1.1)

